Here's a link to the Kentucky form @Mike9241 referred to. You must file this form with your KY employer to prevent KY taxes from being withheld from your pay.
42A809 (ky.gov)
Your employer may or may not be willing to withhold Illinois taxes for you. If Illinois taxes are not withheld from your pay, then you must make quarterly estimated tax payments to Illinois to prevent penalties from being imposed.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
